Dissipation Of MHD Turbulence Research Articles

Coronal Loop Heating by Nearly Incompressible Magnetohydrodynamic and Reduced Magnetohydrodynamic Turbulence Models

The transport of waves and turbulence beyond the photosphere is central to the coronal heating problem. Turbulence in the quiet solar corona has been modeled on the basis of the nearly incompressible magnetohydrodynamic (NI MHD) theory to describe the transport of low-frequency turbulence in open magnetic field regions. It describes the evolution of the coupled majority quasi-2D and minority slab component, driven by the magnetic carpet and advected by a subsonic, sub-Alfvénic flow from the lower corona. In this paper, we couple the NI MHD turbulence transport model with an MHD model of the solar corona to study the heating problem in a coronal loop. In a realistic benchmark coronal loop problem, we find that a loop can be heated to ∼1.5 million K by transport and dissipation of MHD turbulence described by the NI MHD model. We also find that the majority 2D component is as important as the minority slab component in the heating of the coronal loop. We compare our coupled MHD/NI MHD model results with a reduced MHD (RMHD) model. An important distinction between these models is that RMHD solves for small-scale velocity and magnetic field fluctuations and obtains the actual viscous/resistive dissipation associated with their evolution whereas NI MHD evolves scalar moments of the fluctuating velocity and magnetic fields and approximates dissipation using an MHD turbulence phenomenology. Despite the basic differences between the models, their simulation results match remarkably well, yielding almost identical heating rates inside the corona.

CHARACTERISTIC LENGTH OF ENERGY-CONTAINING STRUCTURES AT THE BASE OF A CORONAL HOLE

An essential parameter for models of coronal heating and fast solar wind acceleration that rely on the dissipation of MHD turbulence is the characteristic energy-containing length $\lambda_{\bot}$ of the squared velocity and magnetic field fluctuations ($u^2$ and $b^2$) transverse to the mean magnetic field inside a coronal hole (CH) at the base of the corona. The characteristic length scale defines directly the heating rate. We use a time series analysis of solar granulation and magnetic field measurements inside two CHs obtained with the New Solar Telescope (NST) at Big Bear Solar Observatory. A data set for transverse magnetic fields obtained with the Solar Optical Telescope/Spectro-Polarimeter (SOT/SP) aboard {\it Hinode} spacecraft was utilized to analyze the squared transverse magnetic field fluctuations $b_t^2$. Local correlation tracking (LCT) was applied to derive the squared transverse velocity fluctuations $u^2$. We find that for $u^2$-structures, Batchelor integral scale $\lambda$ varies in a range of 1800 - 2100 km, whereas the correlation length $\varsigma$ and the $e$-folding length $L$ vary between 660 and 1460 km. Structures for $b_t^2$ yield $\lambda \approx 1600$ km, $\varsigma \approx 640$ km, and $L \approx 620$ km. An averaged (over $\lambda, \varsigma$, and $L$) value of the characteristic length of $u^2$-fluctuations is 1260$\pm$500 km, and that of $b_t^2$ is 950$\pm$560 km. The characteristic length scale in the photosphere is approximately 1.5-50 times smaller than that adopted in previous models (3-30$\times10^3$ km). Our results provide a critical input parameter for current models of coronal heating and should yield an improved understanding of fast solar wind acceleration.

Intermittency in MHD turbulence and coronal nanoflares modelling

Abstract. High resolution numerical simulations, solar wind data analysis, and measurements at the edges of laboratory plasma devices have allowed for a huge progress in our understanding of MHD turbulence. The high resolution of solar wind measurements has allowed to characterize the intermittency observed at small scales. We are now able to set up a consistent and convincing view of the main properties of MHD turbulence, which in turn constitutes an extremely efficient tool in understanding the behaviour of turbulent plasmas, like those in solar corona, where in situ observations are not available. Using this knowledge a model to describe injection, due to foot-point motions, storage and dissipation of MHD turbulence in coronal loops, is built where we assume strong longitudinal magnetic field, low beta and high aspect ratio, which allows us to use the set of reduced MHD equations (RMHD). The model is based on a shell technique in the wave vector space orthogonal to the strong magnetic field, while the dependence on the longitudinal coordinate is preserved. Numerical simulations show that injected energy is efficiently stored in the loop where a significant level of magnetic and velocity fluctuations is obtained. Nonlinear interactions give rise to an energy cascade towards smaller scales where energy is dissipated in an intermittent fashion. Due to the strong longitudinal magnetic field, dissipative structures propagate along the loop, with the typical speed of the Alfvén waves. The statistical analysis on the intermittent dissipative events compares well with all observed properties of nanoflare emission statistics. Moreover the recent observations of non thermal velocity measurements during flare occurrence are well described by the numerical results of the simulation model. All these results naturally emerge from the model dynamical evolution without any need of an ad-hoc hypothesis.

Nanoflares and MHD Turbulence in Coronal Loops: A Hybrid Shell Model

A model to describe injection, due to footpoint motions, storage, and dissipation of MHD turbulence in coronal loops, is presented. The model is based on the use of the shell technique in the wave vector space applied to the set of reduced MHD equations. Numerical simulation showed that the energy injected is efficiently stored in the loop where a significant level of magnetic and velocity fluctuations is obtained. Nonlinear interactions among these fluctuations give rise to an energy cascade towards smaller scales where energy is dissipated in an intermittent fashion. The statistical analysis performed on the intermittent dissipative events compares well with all observed properties of nanoflare emission statistics.

Constraints on Stirring and Dissipation of MHD Turbulence in Molecular Clouds

We discuss constraints on the rates of stirring and dissipation of MHD turbulence in molecular clouds. Recent MHD simulations suggest that turbulence in clouds decays rapidly, thus providing a significant source of energy input, particularly if driven at small scales by, for example, bipolar outflows. We quantify the heating rates by combining the line-width-size relations, which describe global cloud properties, with numerically determined dissipation rates. We argue that if cloud turbulence is driven on small internal scales, the 12CO flux (enhanced by emission from weakly supersonic shocks) will be much larger than observed; this, in turn, would imply excitation temperatures significantly above observed values. We reach two conclusions: (1) small-scale driving by bipolar outflows cannot possibly account for cloud support and yield long-lived clouds unless the published MHD dissipation rates are seriously overestimated, and (2) driving on large scales (comparable to the cloud size) is much more viable from an energetic standpoint, and if the actual net dissipation rate is only slightly lower than what current MHD simulations estimate, then the observationally inferred lifetimes and apparent virial equilibrium of molecular clouds can be explained.